Question

What are the amplitude, period, and phase shift of the given function? f(t)=-1/2sin(3t-2pi)

Answer 1

amplitude = 1/2

phase shift = 2/3 pi

period = 2/3 pi

Explanation:

the amplitude is what comes before the sine (but without the negative)

the period is 2pi/B, B here is 3

and the phase shift is -C/B or -(-2)/3 = 2/3 pi

Answer 2

The
`amplitude=|A|=(1)/(2)`,
`period=3` and
`\text{phase shift}=(2\pi)/(3)`.

Explanation:

The given function is

`f(t)=-(1)/(2)\sin (3t-2\pi)` .... (1)

The general form of sine function is

`F(t)=A\sin (Bt-C)+D` ....(2)

where, |A| is the amplitude, B is period, D is the vertical shift (up or down), and C/B is used to find the phase shift.

On comparing (1) and (2), we get

`A=-(1)/(2)`

`B=3`

`C=2\pi`

`D=0`

So,

`amplitude=|A|=(1)/(2)`

`period=3`

`\text{phase shift}=(2\pi)/(3)`

Therefore
`amplitude=|A|=(1)/(2)`,
`period=3` and
`\text{phase shift}=(2\pi)/(3)`.